Barcodes are often used to encode information for various purposes, such as automated part identification. A barcode can be a two-dimensional (e.g., usually rectangular) identifying symbol that includes one or more spatially contiguous sequences of alternating parallel bars and spaces. Each of the bars and spaces is often referred to as an element. A sequence of one or more contiguous elements makes up an element sequence. An element in a barcode element sequence can encode information by its relative width.
Typically, barcodes are created by printing (e.g., with ink) or marking (e.g., by etching) bar elements upon a uniform reflectance substrate (e.g. paper or metal). The bars typically have a lower reflectance than the substrate, and therefore appear darker than the spaces between them (e.g., as when a barcode is printed on white paper using black ink). But barcodes can be printed in other manners, such as when a barcode is printed on a black object using white paint. To differentiate a barcode more readily from the background, the bars are typically placed relatively distant from other printing or visible structures. Such distance creates a space, often referred to as a quiet zone, both prior to the first bar and after the last bar. Alternatively, the spaces and quiet zones can be printed or marked, and the bars are implicitly formed by the substrate.
However, readers often have difficulty decoding barcodes that are under-resolved, such as barcodes that are under-sampled (e.g., due to low sampling rates or low resolution sensors) and/or blurred (e.g., due to poor focus of the reader, or the effects of motion).